to excuse yourself from a conversation without specifying why, for example to leave, buy a drink or go to the bathroom. The original use was to excuse yourself to place a bet on a dog or horse race. The term "see a man about a horse" has the same use.

To politely excuse yourself from a conversation without specifying where you are going. For example if soemone is going to buy a drink or go to the bathroom. It thought to have originated from going to place a bet on a horse or dog race. The term "see a man about a dog' has the same meaning.